If you have the manual for your Case and if turf tires were available as an optional tire, that size should be listed in your Specifications section.
The downside is, those turfs probably won't fit on your current rims.
From TractorData.com:
Ag front: 7.00-16 or 8.00-16
Ag rear: 13.6x24 or 14.9x24
Lawn/turf front: 25x8.50-14 or 27x8.50-15
Lawn/turf rear: 44-18-20
Industrial front: 10x16.5
Industrial rear: 17.5Lx24
Buying tires and rims won't be cheap (if you buy new).
It's going to be some work on your part, but you could call various tire dealers and see if they have a turf tire that will fit your current rims. Don't forget you have to maintain a circumference ratio front to rear so you don't damage your 4WD system.
BTW, are you running the tractor in 4WD on your lawn? Try running in 2WD and don't make tight turns. When I had my old 790 (with R-4's), it would leave impressions in the grass, but they would be gone in a few days. But if I ran in 4WD, the front tires would scuff the grass.